Response to "Battleground Schools"

 (1) The first place I stopped was at Table M1. 

I was reading through the different positions regarding math learning, and a few things came to mind. In the first instance, I was trying to figure out my position on each of those Areas of Interest. I didn't approach the table thinking that my thoughts would align with one column or the other; rather, I tried to see where my initial thoughts landed. (I did, however, in my head replace "conservative" with "old school.") What I noticed is that I too am probably a (closet?) math Platonist. But, slightly to my surprise, I found that my views oscillated between conservative and progressive, and I tried to find the merits in each position. I am interested in this regarding the consistency of my own beliefs regarding math education. I am also prompted to consider whether, in some cases, both outcomes can be produced, even if one outcome may be privileged over another. Furthermore, in trying to find merits in each of the positions, I am encouraged to consider how one could teach and/or assess so that each of those respective positions could be demonstrated.

(2) Another place that I stopped to take a breath was in response to the shift of what mathematics education is for (p. 396). The article introduces Dewey's ideas about privileging inquiry as a way to promote more fully the democratic ideals that were becoming prevalent at that time. Dewey's ideas really did shift what learning could and should look like. I would think that many people may believe that communities of inquiry might be suitable for some aspects of education, but I could understand how there would be pushback from people who think of mathematics as a static, removed set of axioms and ideas. How does inquiry look in mathematics education? It isn't up for debate whether Pythagoras' Theorem is true. And how could we make any progress in mathematics education if each student were asked to 'discover' how a number system worked? In response to this, I want to reply that even in a scenario of a conservative classroom, the teacher still doesn't have so much control over what is actually learned. To teach something and to learn/understand something are different skills. So, by recognizing that people do create the contexts in which they learn, there may be a better discussion for how a democracy or community of inquiry can work in the context of a math education. And, which can often be overlooked, inquiry is not unguided. Providing a rich environment is still a big responsibility of an educator; however, it is worth noting that in this context an educator is not the person who delivers the knowledge. It seems that an educator is more about the person who curates an environment and tests out the resulting ideas. But a potential benefit of adopting some of these ideas is that it places primacy on some skills that will better suit people to participate more fully in a democracy.

(3) The third stop isn't so much a stop as it is an overall response. Who knew that mathematics education could be so politically motivated? In one sense, it really does make sense though. What, after all, is education for? (Maybe Lockhart is right -- that is, maybe math should be an elective.) Every decision that is made in the classroom, even if a teacher or student or parent, is some reflection of some policy decision about something being important. I noticed this after going through an American education system and then teaching in Australia. Different things were taught in Australian classrooms than in American classrooms. That is not to say that fractions were different or that collecting like terms or the FToC were any different. However, some things were very much left absent in different places. Upon reflection, I have found it interesting what is considered important in mathematics education. I also consider the IB math courses. In that programme, math is mandatory. So, it is interesting to see what the curriculum developers feel is important for everyone to know (including those who would not consider themselves mathematically inclined). Furthermore, in a course where, say, graphics calculators are mandatory, it places an emphasis on what skills are promoted. So, in retrospect, it seems initially like a math education is something that might be static; however, a look at other places and times quickly undermines that notion.